In this article, we consider the quasistatic boundary value problems of linear elasticity and nonlinear elastoplasticity, with linear Hooke’s law in the elastic regime for both problems and with the linear kinematic hardening law for the plastic regime in the latter problem. We derive expressions and estimates for the difference of the solutions of both models, i.e. for the stresses, the strains and the displacements. To this end, we use the stop and play operators of nonlinear functional analysis. Further, we give an explicit example of a homotopy between the solutions of both problems.

Simulation of multibody systems (mbs) is an inherent part in developing and design of complex mechanical systems. Moreover, simulation during operation gained in importance in the recent years, e.g. for HIL-, MIL- or monitoring applications. In this paper we discuss the numerical simulation of multibody systems on different platforms. The main section of this paper deals with the simulation of an established truck model [9] on different platforms, one microcontroller and two real-time processor boards. Additional to numerical C-code the latter platforms provide the possibility to build the model with a commercial mbs tool, which is also investigated. A survey of different ways of generating code and equations of mbs models is given and discussed concerning handling, possible limitations as well as performance. The presented benchmarks are processed under terms of on-board real time applications. A further important restriction, caused by the real-time requirement, is a fixed integration step size. Whence, carefully chosen numerical integration algorithms are necessary, especially in the case of closed loops in the model. We investigate linearly-implicit time integration methods with fixed step size, so-called Rosenbrock methods, and compare them with respect to their accuracy and performance on the tested processors.